Consolidation of Clays for Variable Permeability and Compressibility

The theory of consolidation has its origin in the effective stress concept developed by Terzaghi, which was derived based on several assumptions to arrive at a simplified theory. Considering the limitations involved in Terzaghi’s theory, various attempts are being made by researchers to idealize the problem to represent various field situations. This paper presents a more generalized theory for vertical consolidation of a compressible medium of finite thickness, subjected to suddenly applied loading, assuming small strain and no creep. The theory assumes small deformations, and thus the settlement is governed by vertical strains generated by an increment of loading, neglecting the effect of self-weight of the soil. The analytical solution presented here takes into account $e-\log K$ and $e-\log {\sigma }^{\prime }$ linear responses under instantaneous loading. With $C_c$ as the slope of the $e-\log {\sigma }^{\prime }$ line and M the slope of the $e-\log K$ line, a parameter $C_c/M$ is identified which is found to govern the rate of consolidation. In this paper, an analytical closed form solution is obtained for vertical consolidation considering the variation in the compressibility and permeability.